Way Out of EPR: Deterministic Approach to QM.

The basic problem is the base assumption in EPR/Bell formulation, not the results.

EPR paradox   http://en.wikipedia.org/wiki/EPR_paradox

Bell’s work regarding EPR (above article and…).
http://math.ucr.edu/home/baez/physics/Quantum/bells_inequality.html

A single fixed experiment is setup along a single dimension, with detectors oriented in a certain direction – pre-supposing quite innocently the equivalence of any directions in space. While the dimensions of space, XYZ, are equivalent by all measures, they are distinct.

Prepare three Bell experiments – all with the same prepared but random (unmeasured) state source. But each lined up along different XYZ directions. The detectors will use circular polarization (chirality) detection instead of orthogonal axis detection to keep things simple.

Run trials and let the detectors pickup trials. We can go so far as to say the detectors fill up a “hexrant” (pyramid) of space and capture all trials going in that direction (though this grows more impossible as spatial extent of the apparatus is increased). Some previous real-world experiments have rotated a detector pair apparatus in time… that is not germane to this argument.

We can agree that any of the trials go into their respective hexrant pairs in opposite directions. They go into one of the three detector pairs. The others go to other detectors pairs. The only way to get more than a one third yield of trials to any given detector pair is to interfere in the preparation of the states.

Bell’s work and a deterministic hidden variable theory of quantum states can be rationalized if two thirds of the prepared states are lost. They are “lost” into the other hexrant pairs of space. The quantum statistics (where two thirds of trials are lost) can be made to match a hidden variable theory where each test pair member caries with it the information about its state.

The flaw of previous approaches to resolving the EPR paradox were to assume that all directions were equally represented by an experiment in one fixed axis (or even rotating in time but still paired along one axis) . The other directions cannot be ignored.

Many experiments have tried to cover the loss argument by capturing all created states – within the scope of the given axes (at a given time) they are setup against. That is insufficient.

Concrete theories of hidden variables can be developed to explain this apparatus which will completely agree with QM predictions. That is better left to another longer discourse. Here is a simple model for the specific Bell experiments described though…

Assign each trial to each hexrant pair based on its QM compatibility with that axial direction. The “preparedness” of the trials hidden variables will be a mirror, inverse, or reflection of the quantum mechanical result matrix (rotated appropriately in 3D).

Stepping back from the experiment above, one can also view the result as being that quantum mechanics is not “allowing” non-QM results to propagate along any selected axis. The results which do not agree must necessarily be redistributed/rotated to the other axes, to give results according to QM along each and every axes viewed individually (and at any point in time). Directional symmetry and invariance are preserved. 

One can invert this reasoning and say that each prepared trial state outcome is correlated with a given direction within the framework of QM states. Each pair of photons simply has no choice but to go off as QM would send it, and it must go off along an axis compatible with QM. (albeit uniformly in space/time in any statistical group/set).  Again directional symmetry and invariance are preserved. 

Another way of looking at this is to agree that Bell’s theorem is completely correct. The assumptions were correct about the x,y and z being completely commutable in the equations, the trick is in seeing that they are really continuously/actually being commuted trial by trial. That result is the essence of quantum mechanics.

Other variants of the Bell/EPR experiments can be addressed in similar ways in 3D space. (Bohm and Hardy).

The main point of the argument herein is that all states (even/especially ones on orthogonal paths) must be tested for the experiment to be valid against QM assumptions.

The good news is that this twist makes no difference to quantum statistics whatsoever. The unconstrained nature and free propagation of the prepared states was a given, the results are the same as predicted by QM, and what we have stated in no way conflicts with the quantum mechanical interpretation (Copenhagen, Born, etc.). The results do not even conflict with the reasoning of Bell and others. We have not rejected locality nor definiteness. What was missing is the three dimensional nature of space, and that a trial cannot be in three places at once.

Background:

Survey article in Scientific American gelled resolve to try to get out this idea.

von Baeyer, Hans Christian (2013). "Can Quantum Bayesianism Fix the Paradoxes of Quantum Mechanics?". Scientific American 2013 (June). page 46

http://www.scientificamerican.com/article.cfm?id=wave-function

QBism.  http://en.wikipedia.org/wiki/Quantum_Bayesianism